Basic properties
| Modulus: | \(2003\) | |
| Conductor: | \(2003\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(143\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2003.k
\(\chi_{2003}(4,\cdot)\) \(\chi_{2003}(16,\cdot)\) \(\chi_{2003}(42,\cdot)\) \(\chi_{2003}(46,\cdot)\) \(\chi_{2003}(64,\cdot)\) \(\chi_{2003}(88,\cdot)\) \(\chi_{2003}(90,\cdot)\) \(\chi_{2003}(113,\cdot)\) \(\chi_{2003}(121,\cdot)\) \(\chi_{2003}(134,\cdot)\) \(\chi_{2003}(141,\cdot)\) \(\chi_{2003}(142,\cdot)\) \(\chi_{2003}(155,\cdot)\) \(\chi_{2003}(168,\cdot)\) \(\chi_{2003}(174,\cdot)\) \(\chi_{2003}(182,\cdot)\) \(\chi_{2003}(184,\cdot)\) \(\chi_{2003}(185,\cdot)\) \(\chi_{2003}(190,\cdot)\) \(\chi_{2003}(231,\cdot)\) \(\chi_{2003}(256,\cdot)\) \(\chi_{2003}(298,\cdot)\) \(\chi_{2003}(356,\cdot)\) \(\chi_{2003}(360,\cdot)\) \(\chi_{2003}(390,\cdot)\) \(\chi_{2003}(441,\cdot)\) \(\chi_{2003}(452,\cdot)\) \(\chi_{2003}(477,\cdot)\) \(\chi_{2003}(478,\cdot)\) \(\chi_{2003}(479,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{143})$ |
| Fixed field: | Number field defined by a degree 143 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{125}{143}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2003 }(46, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{143}\right)\) | \(e\left(\frac{64}{143}\right)\) | \(e\left(\frac{59}{143}\right)\) | \(e\left(\frac{125}{143}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(e\left(\frac{74}{143}\right)\) | \(e\left(\frac{17}{143}\right)\) | \(e\left(\frac{128}{143}\right)\) | \(e\left(\frac{83}{143}\right)\) | \(e\left(\frac{119}{143}\right)\) |